1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
|
// Copyright (C) 2016 EDF
// All Rights Reserved
// This code is published under the GNU Lesser General Public License (GNU LGPL)
#include <vector>
#include <memory>
#include <iostream>
#include <Eigen/Dense>
#include "StOpt/regression/LocalLinearRegression.h"
#include "StOpt/regression/meshCalculationLocalRegression.h"
#include "StOpt/regression/localLinearMatrixOperation.h"
#include "StOpt/core/grids/InterpolatorSpectral.h"
using namespace std;
using namespace Eigen;
namespace StOpt
{
LocalLinearRegression::LocalLinearRegression(const ArrayXi &p_nbMesh, bool p_bRotationAndRecale): LocalRegression(p_nbMesh, p_bRotationAndRecale) {}
LocalLinearRegression::LocalLinearRegression(const bool &p_bZeroDate,
const ArrayXXd &p_particles,
const ArrayXi &p_nbMesh,
bool p_bRotationAndRecale) : LocalRegression(p_bZeroDate, p_particles, p_nbMesh, p_bRotationAndRecale)
{
if ((!m_bZeroDate) && (p_nbMesh.size() != 0))
{
int nbCell = m_mesh.cols() ;
int iMatrixSize = m_particles.rows() + 1;
// regression matrix
m_matReg = localLinearMatrixCalculation(m_particles, m_simToCell, m_mesh);
// factorize
m_diagReg.resize(iMatrixSize, nbCell);
// utilitary
Array<bool, Dynamic, 1> bSingular(nbCell);
localLinearCholeski(m_matReg, m_diagReg, bSingular) ;
}
}
LocalLinearRegression:: LocalLinearRegression(const LocalLinearRegression &p_object): LocalRegression(p_object), m_matReg(p_object.getMatReg()), m_diagReg(p_object.getDiagReg())
{}
void LocalLinearRegression::updateSimulations(const bool &p_bZeroDate, const ArrayXXd &p_particles)
{
BaseRegression::updateSimulationsBase(p_bZeroDate, p_particles);
m_simToCell.resize(p_particles.cols());
if ((!m_bZeroDate) && (m_nbMesh.size() != 0))
{
if (p_particles.rows() != m_nbMesh.size())
{
cout << " Dimension nd of particles of size (nd, nbSimu) is " << p_particles.rows();
cout << " and should be equal to the size of the array describing the mesh refinement " << m_nbMesh.transpose() << endl ;
abort();
}
meshCalculationLocalRegression(m_particles, m_nbMesh, m_simToCell, m_mesh, m_mesh1D);
int nbCell = m_mesh.cols() ;
int iMatrixSize = m_particles.rows() + 1;
// regression matrix
m_matReg = localLinearMatrixCalculation(m_particles, m_simToCell, m_mesh);
// factorize
m_diagReg.resize(iMatrixSize, nbCell);
// utilitary
Array<bool, Dynamic, 1> bSingular(nbCell);
localLinearCholeski(m_matReg, m_diagReg, bSingular) ;
}
else
{
m_simToCell.setConstant(0);
}
}
ArrayXd LocalLinearRegression::getCoordBasisFunction(const ArrayXd &p_fToRegress) const
{
if ((!m_bZeroDate) && (m_nbMesh.size() != 0))
{
Map<const ArrayXXd> fToRegress2D(p_fToRegress.data(), 1, p_fToRegress.size());
ArrayXXd secMember2D = localLinearSecondMemberCalculation(m_particles, m_simToCell, m_mesh, fToRegress2D);
Map<const ArrayXd > secMember(secMember2D.data(), secMember2D.size());
return localLinearCholeskiInversion(m_matReg, m_diagReg, secMember);
}
else
{
ArrayXd retAverage(1);
retAverage(0) = p_fToRegress.mean();
return retAverage;
}
}
ArrayXXd LocalLinearRegression::getCoordBasisFunctionMultiple(const ArrayXXd &p_fToRegress) const
{
if ((!m_bZeroDate) && (m_nbMesh.size() != 0))
{
ArrayXXd secMember = localLinearSecondMemberCalculation(m_particles, m_simToCell, m_mesh, p_fToRegress);
ArrayXXd regFunc(p_fToRegress.rows(), secMember.cols());
for (int nsm = 0; nsm < p_fToRegress.rows(); ++nsm)
{
ArrayXd secMemberLoc(secMember.cols());
secMemberLoc = secMember.row(nsm);
regFunc.row(nsm) = localLinearCholeskiInversion(m_matReg, m_diagReg, secMemberLoc).transpose();
}
return regFunc;
}
else
{
ArrayXXd retAverage(p_fToRegress.rows(), 1);
for (int nsm = 0; nsm < p_fToRegress.rows(); ++nsm)
retAverage.row(nsm).setConstant(p_fToRegress.row(nsm).mean());
return retAverage;
}
}
ArrayXd LocalLinearRegression::reconstruction(const ArrayXd &p_basisCoefficients) const
{
if ((!m_bZeroDate) && (m_nbMesh.size() != 0))
{
Map<const ArrayXXd> BasisCoefficients(p_basisCoefficients.data(), 1, p_basisCoefficients.size());
return localLinearReconstruction(m_particles, m_simToCell, m_mesh, BasisCoefficients).row(0);
}
else
return ArrayXd::Constant(m_simToCell.size(), p_basisCoefficients(0));
}
ArrayXXd LocalLinearRegression::reconstructionMultiple(const ArrayXXd &p_basisCoefficients) const
{
if ((!m_bZeroDate) && (m_nbMesh.size() != 0))
{
return localLinearReconstruction(m_particles, m_simToCell, m_mesh, p_basisCoefficients);
}
else
{
ArrayXXd retValue(p_basisCoefficients.rows(), m_simToCell.size());
for (int nsm = 0; nsm < p_basisCoefficients.rows(); ++nsm)
retValue.row(nsm).setConstant(p_basisCoefficients(nsm, 0));
return retValue ;
}
}
double LocalLinearRegression::reconstructionASim(const int &p_isim, const ArrayXd &p_basisCoefficients) const
{
if ((!m_bZeroDate) && (m_nbMesh.size() != 0))
{
return localLinearReconstructionASim(p_isim, m_particles, m_simToCell, m_mesh, p_basisCoefficients);
}
else
{
return p_basisCoefficients(0);
}
}
ArrayXd LocalLinearRegression::getAllSimulations(const ArrayXd &p_fToRegress) const
{
Map<const ArrayXXd> fToRegress2D(p_fToRegress.data(), 1, p_fToRegress.size());
ArrayXXd BasisCoefficients = getCoordBasisFunctionMultiple(fToRegress2D);
if ((m_bZeroDate) || (m_nbMesh.size() == 0))
{
return ArrayXd::Constant(p_fToRegress.size(), BasisCoefficients(0, 0));
}
ArrayXXd condEspectationValues = localLinearReconstruction(m_particles, m_simToCell, m_mesh, BasisCoefficients);
return condEspectationValues.row(0);
}
ArrayXXd LocalLinearRegression::getAllSimulationsMultiple(const ArrayXXd &p_fToRegress) const
{
ArrayXXd BasisCoefficients = getCoordBasisFunctionMultiple(p_fToRegress);
if ((m_bZeroDate) || (m_nbMesh.size() == 0))
{
ArrayXXd ret(p_fToRegress.rows(), p_fToRegress.cols());
for (int ism = 0; ism < p_fToRegress.rows(); ++ism)
ret.row(ism).setConstant(BasisCoefficients(ism, 0));
return ret;
}
return localLinearReconstruction(m_particles, m_simToCell, m_mesh, BasisCoefficients);
}
ArrayXd LocalLinearRegression::getAllSimulationsConvex(const ArrayXd &p_fToRegress, const int &p_nbIterMax)
{
if ((m_bZeroDate) || (m_nbMesh.size() == 0))
return ArrayXd::Constant(p_fToRegress.size(), p_fToRegress.mean());
// number of cells
int nbCell = m_mesh.cols() ;
// utilitary
Array<bool, Dynamic, 1> bSingular(nbCell);
// eigen map to avoid copy
Map<const ArrayXXd> fToRegress2D(p_fToRegress.data(), 1, p_fToRegress.size());
// error
double error = 1e6;
// iteration number
int iterN = 0 ;
// to store old position
ArrayXi simToCellOld = m_simToCell;
// second member
ArrayXXd BasisCoefficients = getCoordBasisFunctionMultiple(fToRegress2D);
// iterate on the regressions
while ((error > 0) && (iterN++ < p_nbIterMax))
{
localLinearConvexHull(m_particles, m_mesh, BasisCoefficients, nbCell, m_simToCell);
// update error
error = (simToCellOld - m_simToCell).abs().sum();
if (error > 0)
{
// update matrix
m_matReg = localLinearMatrixCalculation(m_particles, m_simToCell, m_mesh);
// utilitary
localLinearCholeski(m_matReg, m_diagReg, bSingular) ;
// second member update
BasisCoefficients = getCoordBasisFunctionMultiple(fToRegress2D);
}
// keep position
simToCellOld = m_simToCell;
}
// final reconstrucion
ArrayXXd condEspectationValues = localLinearReconstruction(m_particles, m_simToCell, m_mesh, BasisCoefficients);
return condEspectationValues.row(0);
}
double LocalLinearRegression::getValue(const ArrayXd &p_coordinates, const ArrayXd &p_coordBasisFunction) const
{
if ((!m_bZeroDate) && (m_nbMesh.size() != 0))
{
// rotation
VectorXd x = m_svdMatrix * ((p_coordinates - m_meanX) / m_etypX).matrix();
Map<const ArrayXXd> coordBasisFunction2D(p_coordBasisFunction.data(), 1, p_coordBasisFunction.size());
return localLinearReconstructionOnePoint(x.array(), m_mesh1D, coordBasisFunction2D)(0);
}
else
{
return p_coordBasisFunction(0);
}
}
double LocalLinearRegression::getAValue(const ArrayXd &p_coordinates, const ArrayXd &p_ptOfStock,
const vector< shared_ptr<InterpolatorSpectral> > &p_interpFuncBasis) const
{
if ((!m_bZeroDate) && (m_nbMesh.size() != 0))
{
// rotation
VectorXd x = m_svdMatrix * ((p_coordinates - m_meanX) / m_etypX).matrix();
return localLinearReconsOnePointSimStock(x, p_ptOfStock, p_interpFuncBasis, m_mesh1D);
}
else
{
return p_interpFuncBasis[0]->apply(p_ptOfStock);
}
}
ArrayXd LocalLinearRegression::getCoordBasisFunctionOneCell(const int &p_iCell, const ArrayXd &p_fToRegress) const
{
if ((!m_bZeroDate) && (m_nbMesh.size() != 0))
{
Map<const ArrayXXd> fToRegress2D(p_fToRegress.data(), 1, p_fToRegress.size());
ArrayXXd secMember2D = localLinearSecondMemberCalculationOneCell(m_particles, *(m_simulBelongingToCell[p_iCell]), m_mesh.col(p_iCell), fToRegress2D);
Map<const ArrayXd > secMember(secMember2D.data(), secMember2D.size());
return localLinearCholeskiInversionOneCell(p_iCell, m_matReg, m_diagReg, secMember);
}
else
{
ArrayXd retAverage(1);
retAverage(0) = p_fToRegress.mean();
return retAverage;
}
}
ArrayXXd LocalLinearRegression::getCoordBasisFunctionMultipleOneCell(const int &p_iCell, const ArrayXXd &p_fToRegress) const
{
if ((!m_bZeroDate) && (m_nbMesh.size() != 0))
{
ArrayXXd secMember = localLinearSecondMemberCalculationOneCell(m_particles, *(m_simulBelongingToCell[p_iCell]), m_mesh.col(p_iCell), p_fToRegress);
// normalization
secMember /= m_particles.cols();
ArrayXXd regFunc(p_fToRegress.rows(), secMember.cols());
for (int nsm = 0; nsm < p_fToRegress.rows(); ++nsm)
{
ArrayXd secMemberLoc(secMember.cols());
secMemberLoc = secMember.row(nsm);
regFunc.row(nsm) = localLinearCholeskiInversionOneCell(p_iCell, m_matReg, m_diagReg, secMemberLoc).transpose();
}
return regFunc;
}
else
{
ArrayXXd retAverage(p_fToRegress.rows(), 1);
for (int nsm = 0; nsm < p_fToRegress.rows(); ++nsm)
retAverage.row(nsm).setConstant(p_fToRegress.row(nsm).mean());
return retAverage;
}
}
ArrayXd LocalLinearRegression::getValuesOneCell(const ArrayXd &p_oneParticle, const int &p_cell, const ArrayXXd &p_foncBasisCoef) const
{
if ((!m_bZeroDate) && (m_nbMesh.size() != 0))
{
// rotation
VectorXd x = p_oneParticle.matrix();
x = ((x.array() - m_meanX) / m_etypX).matrix();
x = m_svdMatrix * x;
return localLinearReconstructionOnePointOneCell(x.array(), m_mesh.col(p_cell), p_foncBasisCoef);
}
else
{
return p_foncBasisCoef.col(0);
}
}
}
|
